Are backpack and tool upgrades separate or shared among players?
Tool and backpack upgrades are separate for each player. It does get expensive fast to have to spend a few thousand gold and metal bars several times, but it is worth noting that you can share your tools with you friends by placing them in a chest, since anyone can access any chest.
As a side note, while Clint is upgrading a tool, he will still be open for business (shopping, upgrading, cracking geodes) for players who are not having their tool upgraded.
Source: I've already spent over a whole season in multiplayer with friends.